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Abstract  

Egghe's continuous information production processes (in short IPP's) are described using category theory. Therefore, we first review the main ingredients of this mathematical theory, introduced byEilenberg andMac Lane more than four decades ago. Then we show how the notion of duality, as used byEgghe, can be placed in the abstract framework of categorical duality. This leads to a natural isomorphism involving the identity functor on a category of continuous IPP's. This natural isomorphism is completely similar to the well-known natural isomorphism between a finite-dimensional vector space and its double dual. We further show that to develop Egghe's theory on IPP's one needs no other intervals than the unit interval.

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Abstract  

In this note we show that the special class generated by a prime PI-ring is, up to isomorphism, a left and right equivalence class of orders in some matrix quotient ring.

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Journal of Radioanalytical and Nuclear Chemistry
Authors:
Y. Kobayashi
,
Y. Tsuruoka
,
M. Kubo
,
H. Nonaka
,
Y. Yamada
,
Y. Sakai
,
H. Shoji
,
W. Sato
,
A. Shinohara
,
Y. Watanabe
, and
H. Matsue

Abstract  

In order to investigate the physical and chemical effects of neutron capture reaction, a neutron in-beam Mössbauer spectroscopic study on two isomorphs of iron disulfide: pyrite and marcasite, were carried out with a parallel plate avalanche counter at room temperature. In both compounds only two major products accounted for the obtained spectrum: one with Mössbauer parameters close to the parent compound and the other one considered to be a new product. The yield of the parent-like species was different in the two isomorphs.

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Abstract  

Let R denote the purely infinite simple unital Leavitt path algebra L(E). We completely determine the pairs of positive integers (c, d) for which there is an isomorphism of matrix rings M c (R) ≌ M d (R), in terms of the order of [1 R ] in the Grothendieck group K 0(R).

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A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.

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] Jayne , J. E. , Rogers , C. A. 1982 First level Borel functions and isomorphisms J. Math. Pures et Appl. 61 177 – 205 . [3] Mill van , J. , Pol , R. 1995 Baire 1 functions which are

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Abstract  

We prove that there exists a special homeomorphism of the Cantor space such that every noncancellable composition of finite powers and translations of rational numbers has no fixed point. For this homeomorphism there exists both a Vitali and Bernstein subset of the Cantor set such that the image of this set is equal to its complement. There exists a Bernstein and Vitali set such that there is no Borel isomorphism between this set and its complement.

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An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element x such that x and x 2 are linearly independent. We list all multiplication tables of the algebras up to isomorphism.

Open access
Journal of Thermal Analysis and Calorimetry
Authors:
D. Gouveia
,
A. Souza
,
M. de Maurera
,
C. da Costa
,
I. Santos
,
S. Prasad
,
J. de Lima
,
C. Paskocimas
, and
E. Longo

Abstract  

Using the Pechini method, pigments with spinel structure (Zn7Sb2O12)were synthesized by substitution of the cation Zn2+ by Co2+, in compounds with different concentrations of Sb2O3. The doping resulted in CoxZn(7–x)Sb2O12 phases(x=1–7) that were isomorphs to spinel, denominated as samples A and B. After thermal treatment at 400C for 1 h, the powders were characterized by thermogravimetry(TG) and differential thermal analysis (DTA). The results indicate a different behavior whena higher amount of Sb2O3 is used, due to the presence of a secondary phase (ilmenite).

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Hydrazinium metal glycinates [(N2H5 2M(NH2CH2COO)4] and bis(hydrazine)metal glycinates, [M(NH2CH2COO)2(N2H4)2], whereM=Co, Ni or Zn have been prepared and characterized by chemical analyses, magnetic moments and vibrational and electronic spectra. The thermal behaviour of these compounds has been studied by thermogravimetry and differential thermal analyses. These complexes decompose with high exothermicity giving metal powder as the final residue. The X-ray powder data of each set of complexes show isomorphism among themselves.

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